Aggregates of two-dimensional vesicles: rouleaux, sheets, and convergent extension

Mechanical stiffening of porphyrin nanorings through supramolecular columnar stacking

Solvent-induced aggregates of nanoring cyclic polymers may be transferred by electrospray deposition to a surface where they adsorb as three-dimensional columnar stacks. The observed stack height varies from single rings to four stacked rings with a layer spacing of 0.32 ± 0.04 nm as measured using scanning tunneling microscopy. The flexibility of the nanorings results in distortions from a circular shape, and we show, through a comparison with Monte Carlo simulations, that the bending stiffness increases linearly with the stack height. Our results show that noncovalent interactions may be used to control the shape and mechanical properties of artificial macromolecular aggregates offering a new route to solvent-induced control of two-dimensional supramolecular organization.

Periodic three-dimensional assemblies of polyhedral lipid vesicles

We theoretically study the structure of periodic bulk assemblies of identical lipid vesicles. In our model, each vesicle is represented as a convex polyhedron with flat faces, rounded edges, and rounded vertices. Each vesicle carries an elastic and an adhesion energy and in the limit of strong adhesion, the minimal-energy shape of cells minimizes the weighted total edge length. We calculate exactly the shape of the rounded edge and show that it can be well described by a cylindrical surface. By comparing several candidate space-filling polyhedra, we find that the oblate shapes are preferred over prolate shapes for all volume-to-surface ratios. We also study periodic assemblies of vesicles whose adhesion strength on lateral faces is different from that on basal or apical faces. The anisotropy needed to stabilize prolate shapes is determined and it is shown that, at any volume-to-surface ratio, the transition between oblate and prolate shapes is very sharp. The geometry of the model vesicle assemblies reproduces the shapes of cells in certain simple animal tissues.

Adhesive interactions between vesicles in the strong adhesion limit

We consider the adhesive interaction energy between a pair of vesicles in the strong adhesion limit, in which bending forces play a negligible role in determining vesicle shape compared to forces due to membrane stretching. Although force−distance or energy−distance relationships characterizing adhesive interactions between fluid bilayers are routinely measured using the surface forces apparatus, the atomic force microscope, and the biomembrane force probe, the interacting bilayers in these methods are supported on surfaces (e.g., mica sheet) and cannot be deformed. However, it is known that, in a suspension, vesicles composed of the same bilayer can deform by stretching or bending, and can also undergo changes in volume. Adhesively interacting vesicles can thus form flat regions in the contact zone, which will result in an enhanced interaction energy as compared to rigid vesicles. The focus of this paper is to examine the magnitude of the interaction energy between adhesively interacting, deformed vesicles relative to free, undeformed vesicles as a function of the intervesicle separation. The modification of the intervesicle interaction energy due to vesicle deformability can be calculated knowing the undeformed radius of the vesicles, R0, the bending modulus, k(b), the area expansion modulus, k(a), and the adhesive minimum, W(P)(0), and separation, D(P)(0), in the energy of interaction between two flat bilayers, which can be obtained from the force−distance measurements made using the above supported-bilayer methods. For vesicles with constant volumes, we show that adhesive potentials between nondeforming bilayers such as |W(P)(0)| 5 × 10(−4) mJ/m2, which are ordinarily considered weak in the colloidal physics literature, can result in significantly deep (>10×) energy minima due to increase in vesicle area and flattening in the contact region. If the osmotic expulsion of water across the vesicles driven by the tense, stretched membrane in the presence of an osmotically active solute is also taken into account, the vesicles can undergo additional deformation (flattening), which further enhances the adhesive interaction between them. Finally, equilibration of ions and solutes due to the concentration differences created by the osmotic exchange of water can lead to further enhancement of the adhesion energy. Our result of the progressively increasing adhesive interaction energy between vesicles in the above regimes could explain why suspensions of very weakly attractive vesicles may undergo flocculation and eventual instability due to separation of vesicles from the suspending fluid by gravity. The possibility of such an instability is an extremely important issue for concentrated vesicle-based products and applications such as fabric softeners, hair therapeutics and drug delivery.